Special subset sums: optimum Let S(A) represent the sum of elements in set A of size n. We shall call it a special sum set if for any two non-empty disjoint subsets, B and C, the following properties are true: S(B) ≠ S(C); that is, sums of subsets ca…

Special subset sums: meta-testing Let S(A) represent the sum of elements in set A of size n. We shall call it a special sum set if for any two non-empty disjoint subsets, B and C, the following properties are true: S(B) ≠ S(C); that is, sums of subse…

Special subset sums: testing Let S(A) represent the sum of elements in set A of size n. We shall call it a special sum set if for any two non-empty disjoint subsets, B and C, the following properties are true: S(B) ≠ S(C); that is, sums of subsets ca…

本题来自 Project Euler 第9题:https://projecteuler.net/problem=9 # Project Euler: Problem 9: Special Pythagorean triplet # A Pythagorean triplet is a set of three natural numbers, # a < b < c, for which, a**2 + b**2 = c**2 # For example, 3**2 + 4**2 = 9 +…

上一次接触 project euler 还是2011年的事情,做了前三道题,后来被第四题卡住了,前面几题的代码也没有保留下来. 今天试着暴力破解了一下,代码如下: (我大概是第 172,719 个解出这道题的人) program 4 A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99.…

P1466 集合 Subset Sums 162通过 308提交 题目提供者该用户不存在 标签USACO 难度普及/提高- 提交  讨论  题解 最新讨论 暂时没有讨论 题目描述 对于从1到N (1 <= N <= 39) 的连续整数集合,能划分成两个子集合,且保证每个集合的数字和是相等的.举个例子,如果N=3,对于{1,2,3}能划分成两个子集合,每个子集合的所有数字和是相等的: {3} 和 {1,2} 这是唯一一种分法(交换集合位置被认为是同一种划分方案,因此不会增加划分方案总数) 如果N…

开始做 Project Euler 的练习题.网站上总共有565题,真是个大题库啊! # Project Euler, Problem 1: Multiples of 3 and 5 # If we list all the natural numbers below 10 # that are multiples of 3 or 5, we get 3, 5, 6 and 9. # The sum of these multiples is 23. # Find the sum of all…

题意:三个正整数a + b + c = 1000,a*a + b*b = c*c.求a*b*c. 解法:可以暴力枚举,但是也有数学方法. 首先,a,b,c中肯定有至少一个为偶数,否则和不可能为以上两个等式均不会成立.然后,不可能a,b为奇c为偶,否则a*a%4=1, b*b%4=1, 有(a*a+b*b) %4 = 2,而c*c%4 = 0.也就是说,a和b中至少有一个偶数. 这是勾股数的一个性质,a,b中至少有一个偶数. 然后,解决过程见下(来自project euler的讨论): tag:m…

Portal Description 给出长度为\(n(n\leq10^5)\)的序列\(\{a_n\}\)以及\(m(m\leq10^5)\)个下标集合\(\{S_m\}(\sum|S_i|\leq10^5)\),进行\(q(q\leq10^5)\)次操作: 询问下标属于集合\(S_k\)的所有数之和. 将下标属于集合\(S_k\)的所有数加\(x\). Solution 记\(N_0=\sqrt{\sum|S_i|}\). 我们把集合划分成轻集合与重集合,大小超过\(N_0\)的集合就是重集…

In Problem 42 we dealt with triangular problems, in Problem 44 of Project Euler we deal with pentagonal number, I can only wonder if we have to deal with septagonal numbers in Problem 46. Anyway the problem reads Pentagonal numbers are generated by t…